The hard-disk fluid revisited

TL;DR

This paper uses large-scale molecular dynamics simulations to analyze the transport properties of the hard-disk model, revealing deviations from traditional theories and proposing a unified, parameter-free expression that bridges kinetic and hydrodynamic approaches.

Contribution

It introduces a unified theoretical framework that accurately describes autocorrelation functions across all time scales and densities, improving upon conventional transport theories.

Findings

Significant deviations from conventional predictions at higher densities.

A new parameter-free expression for velocity autocorrelation functions.

Bridging kinetics and hydrodynamics in transport theory.

Abstract

The hard-disk model plays a role of touchstone for testing and developing the transport theory. By large scale molecular dynamics simulations of this model, three important autocorrelation functions, and as a result the corresponding transport coefficients, i.e., the diffusion constant, the thermal conductivity and the shear viscosity, are found to deviate significantly from the predictions of the conventional transport theory beyond the dilute limit. To improve the theory, we consider both the kinetic process and the hydrodynamic process in the whole time range, rather than each process in a seperated time scale as the conventional transport theory does. With this consideration, a unified and coherent expression free of any fitting parameters is derived succesfully in the case of the velocity autocorrelation function, and its superiority to the conventional `piecewise' formula is shown. This expression applies to the whole time range and up to moderate densities, and thus bridges the kinetics and hydrodynamics approaches in a self-consistent manner.